As is known in the art, magnetic resonance imaging (MRI) (aka nuclear magnetic resonance or NMR) is a form of medical imaging in which the data is displayed as images which are presented in the form of individual slices that represent planar sections of objects. The data in the images represents the density and bonding of protons (primarily in water) in the tissues of the body, based upon the ability of certain atomic nuclei in a magnetic field to absorb and re-emit electromagnetic radiation at certain frequencies.
As is also known, MRI is based on the magnetic properties of atomic nuclei with odd numbers of protons or neutrons, which exhibit magnetic properties because of their spin. The predominant source of magnetic resonance signals in the human body is hydrogen nuclei or protons. In the presence of an external magnetic field these hydrogen nuclei align along the axis of the external magnetic field and can precess or wobble around that field direction at a definite frequency known as the Larmor frequency.
The magnetic resonance effects occur when nuclei in a static magnetic field H are excited by a rotating magnetic field H1 in the x, y plane resulting in a total vector M given by M=Hz+H1(×cos w0t+y sin w0t). Upon cessation of the excitation, the magnetic field decays back to its original alignment with the static field H, emitting electromagnetic radiation at the Larmor frequency which can be detected by the same coil which produced the excitation.
One method for imaging utilizes a transmit/receive coil to emit a magnetic field at frequency f0 which is the Larmor frequency of plane P. Subsequently, magnetic gradients are applied in the y and x directions Gx, Gy for times tx, ty. A signal is detected in a data collection window over the period of time for which a magnetic gradient Gx is applied.
The detected signal S(tx, ty) can be expressed as a two-dimensional Fourier transform of the magnetic resonance signal s(x,y) with u=γGxtx/2π, v=γGyty/2π. The magnetic resonance signal s(x,y) depends on the precise sequence of pulses of magnetic energy used to perturb the nuclei.
For a typical sequence known as spin-echo the detected magnetic resonance signal can be expresseds(x,y)=ρ(1−e−tr/T1)(e−tr/T2)
where ρ is the proton density, and T1 (the spin-lattice decay time) and T2 (the spin-spin decay time) are constants of the material related to the interactions of water in cells. Typically T1 ranges from 0.2 to 1.2 seconds, while T2 ranges from 0.05 to 0.15 seconds.
By modification of the repetition and orientation of excitation pulses, an image can be made T1, T2, or proton density dominated. A proton density image shows static blood and fat as white and bone as black, while a T1 weighted image shows fat as white, blood as gray, and cerebrospinal fluid as black and T2 weighted images tend to highlight pathology since pathologic tissue tends to have longer T2 than normal tissue.
To measure spin-spin decay or relaxation time (T2) a technique referred to as the spin echo technique was developed. The spin-echo technique includes the steps of applying an RF pulse sequence at the Larmor frequency of the nuclei, whose T2 is being measured. The first RF pulse is sufficient duration to force the net magnetic moment of the nuclei to rotate 90°. This is followed by one or more RF pulses at the same Larmor frequency of sufficient duration to rotate the net magnetic field 180°. After each 180° pulse a signal referred to as a “spin-echo signal” is produced. The T2 relaxation time of the nuclei is indicated by the curve drawn through the points of maximum amplitude of the echo signals received.
This technique would produce an accurate measurement of T2 if the RF magnetic field was uniform at the same Larmor frequency because then only one spin-echo signal would be generated with each 180° pulse. Unfortunately, the RF magnetic field is not uniform. For example, some portions of the RF field may be at the Larmor frequency but other portions may be at a higher or lower frequency. It is believed that as a result of this, the inhomogeneities in the RF magnetic field produce so-called “stimulated echos” in addition to the primary echos.
In the present practice of the spin-echo technique for measuring T2, after the 90° pulse, the first 180° pulse occurs after a time period, usually called “tau.” Stimulated echos, however, can appear at these same times and when they do, they will be masked by and mingled with the primary echos. As a result, the degree of error in the measured T2 is unknown. Because of the errors caused by inhomogeneities in the static and RF magnetic fields of NMR machines, it is thus not possible to directly measure the T2 relaxation time (T2 RT) with a reasonable degree of certainty or accuracy.